The property is Outlook.MailItem.TaskCompletedDate. Try something like:
Sub GetCompletedToday()
Dim olNameSpace As Outlook.NameSpace
Dim olFolder As Outlook.Folder
Dim olMailItem As Outlook.MailItem
Dim CompletedTodayCount As Long
Set olNameSpace = Application.GetNamespace("MAPI")
Set olFolder = olNameSpace.Folders(1).Folders("tester")
For Each olMailItem In olFolder.Items
If olMailItem.TaskCompletedDate = Date Then
CompletedTodayCount = CompletedTodayCount + 1
End If
Next olMailItem
Debug.Print CompletedTodayCount
End Sub
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